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### 12 Making Trees Grow

#### 12.1 Introduction to the Child Operation

Trees are a common way of visualizing hierarchical structures. A simple tree looks like this:

\begin{tikzpicture} \node {root} child {node {left}} child {node {right} child {node {child}}
child {node {child}}
};
\end{tikzpicture}

Admittedly, in reality trees are more likely to grow upward and not downward as above. You can tell whether the author of a paper is a mathematician or a computer scientist by looking at the direction their trees grow. A computer scientist’s trees will grow downward while a mathematician’s tree will grow upward. Naturally, the correct way is the mathematician’s way, which can be specify as follows:

\begin{tikzpicture} \node {root} [grow'=up] child {node {left}} child {node {right} child {node {child}}
child {node {child}}
};
\end{tikzpicture}

In TikZ, trees are specified by adding children to a node on a path using the child operation:

\path ... child[<options>]foreach<variables>in{<values>}{<child path>} ...;

  This operation should directly follow a completed node operation or another child operation, although it is permissible that the first child operation is preceded by options (we will come to that).

  When a node operation like node {X} is followed by child, TikZ starts counting the number of child nodes that follow the original node {X}. For this, it scans the input and stores away each child and its arguments until it reaches a path operation that is not a child. Note that this will fix the character codes of all text inside the child arguments, which means, in essence, that you cannot use verbatim text inside the nodes inside a child. Sorry.

  Once the children have been collected and counted, TikZ starts generating the child nodes. For each child of a parent node TikZ computes an appropriate position where the child is placed. For each child, the coordinate system is transformed so that the origin is at this position. Then the <child path> is drawn. Typically, the child path just consists of a node specification, which results in a node being drawn at the child’s position. Finally, an edge is drawn from the first node in the <child path> to the parent node.

  The optional foreach part (note that there is no backslash before foreach) allows you to specify multiple children in a single child command. The idea is the following: A \foreach statement is (internally) used to iterate over the list of <values>. For each value in this list, a new child is added to the node. The syntax for <variables> and for <values> is the same as for the \foreach statement, see Section 15. For example, when you say

  node {root} child [red] foreach \name in {1,2} {node {\name}}

  the effect will be the same as if you had said

  node {root} child[red] {node {1}} child[ref] {node {2}}

  When you write

  node {root} child[\pos] foreach \name/\pos in {1/left,2/right} {node[\pos] {\name}}

  the effect will be the same as for

  node {root} child[left] {node[left] {1}} child[right] {node[right] {2}}

  You can nest things as in the following example:

  \begin{tikzpicture}[level distance=4mm] \tikzstyle{level 1}=[sibling distance=8mm] \tikzstyle{level 2}=[sibling distance=4mm] \tikzstyle{level 3}=[sibling distance=2mm] \coordinate
  child foreach \x in {0,1}
  {child foreach \y in {0,1}
  {child foreach \z in {0,1}}};
  \end{tikzpicture}

  The details and options for this operation are described in the rest of this present section.

#### 12.2 Child Paths and the Child Nodes

For each child of a root node, its <child path> is inserted at a specific location in the picture (the placement rules are discussed in Section 12.5). The first node in the <child path>, if it exists, is special and called the child node. If there is no first node in the <child path>, that is, if the <child path> is missing (including the curly braces) or if it does not start with node or with coordinate, then an empty child node of shape coordinate is automatically added.

Consider the example \node {x} child {node {y}} child;. For the first child, the <child path> has the child node node {y}. For the second child, no child node is specified and, thus, it is just coordinate.

As for any normal node, you can give the child node a name, shift it around, or use options to influence how it is rendered.

\begin{tikzpicture} \node[rectangle,draw] {root} child {node[circle,draw] (left node) {left}} child {node[ellipse,draw] (right node) {right}}; \draw[dashed,->] (left node) -- (right node);
\end{tikzpicture}

In many cases, the <child path> will just consist of a specification of a child node and, possibly, children of this child node. However, the node specification may be followed by arbitrary other material that will be added to the picture, transformed to the child’s coordinate system. For your convenience, a move-to (0,0) operation is inserted automatically at the beginning of the path. Here is an example:

\begin{tikzpicture} \node {root} child {[fill] circle (2pt)} child {[fill] circle (2pt)}; \end{tikzpicture}

At the end of the <child path> you may add a special path operation called edge from parent. If this operation is not given by yourself somewhere on the path, it will be automatically added at the end. This option causes a connecting edge from the parent node to the child node to be added to the path. By giving options to this operation you can influence how the edge is rendered. Also, nodes following the edge from parent operation will be placed on this edge, see Section 12.6 for details.

To sum up:

1. The child path starts with a node specification. If it is not there, it is added automatically.
2. The child path ends with a edge from parent operation, possibly followed by nodes to be put on this edge. If the operation is not given at the end, it is added automatically.

#### 12.3 Naming Child Nodes

Child nodes can be named like any other node using either the name option or the special syntax in which the name of the node is placed in round parentheses between the node operation and the node’s text.

If you do not assign a name to a child node, TikZ will automatically assign a name as follows: Assume that the name of the parent node is, say, parent. (If you did not assign a name to the parent, TikZ will do so itself, but that name will not be user-accessible.) The first child of parent will be named parent-1, the second child is named parent-2, and so on.

This naming convention works recursively. If the second child parent-2 has children, then the first of these children will be called parent-2-1 and the second parent-2-2 and so on.

If you assign a name to a child node yourself, no name is generated automatically (the node does not have two names). However, “counting continues,” which means that the third child of parent is called parent-3 independently of whether you have assigned names to the first and/or second child of parent.

Here is an example:

\begin{tikzpicture} \node (root) {root} child child { child {coordinate (special)}
child
};
\node at (root-1) {root-1};
\node at (root-2) {root-2};
\node at (special) {special};
\node at (root-2-2) {root-2-2};
\end{tikzpicture}

#### 12.4 Specifying Options for Trees and Children

Each child may have its own <options>, which apply to “the whole child,” including all of its grandchildren. Here is an example:

\begin{tikzpicture}[thick] \tikzstyle{level 2}=[sibling distance=10mm] \coordinate child[red] {child child} child[green] {child child[blue]};
\end{tikzpicture}

The options of the root node have no effect on the children since the options of a node are always “local” to that node. Because of this, the edges in the following tree are black, not red.

\begin{tikzpicture}[thick] \node [red] {root} child child; \end{tikzpicture}

This raises the problem of how to set options for all children. Naturally, you could always set options for the whole path as in \path [red] node {root} child child; but this is bothersome in some situations. Instead, it is easier to give the options before the first child as follows:

\begin{tikzpicture}[thick] \node [red] {root} [green] % option applies to all children child child;
\end{tikzpicture}

Here is the set of rules:

1. Options for the whole tree are given before the root node.
2. Options for the root node are given directly to the node operation of the root.
3. Options for all children can be given between the root node and the first child.
4. Options applying to a specific child path are given as options to the child operation.
5. Options applying to the node of a child, but not to the whole child path, are given as options to the node command inside the <child path>.

\begin{tikzpicture} \path [...] % Options apply to the whole tree node[...] {root} % Options apply to the root node only [...] % Options apply to all children
child[...] % Options apply to this child and all its children
{
node[...] {} % Options apply to the child node only
...
}
child[...] % Options apply to this child and all its children
;
\end{tikzpicture}

There are additional styles that influence how children are rendered:

- style=every child This style is used at the beginning of each child, as if you had given the options to the child operation.
- style=every child node This style is used at the beginning of each child node in addition to the every node style.
- style=level <number> This style is used at the beginning of each set of children, where <number> is the current level in the current tree. For example, when you say \node {x} child child;, then the style level 1 is used before the first child. If this first child has children itself, then level 2 would be used for them.

  \begin{tikzpicture} \tikzstyle{level 1}=[sibling distance=20mm] \tikzstyle{level 2}=[sibling distance=5mm] \node {root} child { child child }
  child { child child child };
  \end{tikzpicture}

#### 12.5 Placing Child Nodes

Perhaps the most difficult part in drawing a tree is the correct layout of the children. Typically, the children have different sizes and it is not easy to arrange them in such a manner that not too much space is wasted, the children do not overlap, and they are either evenly spaced or their centers are evenly distributed. Calculating good positions is especially difficult since a good position for the first child may depend on the size of the last child.

In TikZ, a comparatively simple approach is taken to placing the children. In order to compute a child’s position, all that is taken into account is the number of the current child in the list of children and the number of children in this list. Thus, if a node has five children, then there is a fixed position for the first child, a position for the second child, and so on. These positions do not depend on the size of the children and, hence, children can easily overlap. However, since you can use options to shift individual children a bit, this is not as great a problem as it may seem.

Although the placement of the children only depends on their number in the list of children and the total number of children, everything else about the placement is highly configurable. You can change the distance between children (appropriately called the sibling distance) and the distance between levels of the tree. These distances may change from level to level. The direction in which the tree grows can be changed globally and for parts of the tree. You can even specify your own “growth function” to arrange children on a circle or along special lines or curves.

The default growth function works as follows: Assume that we are given a node and five children. These children will be placed on a line with their centers (or, more generally, with their anchors) spaced apart by the current sibling distance. The line is orthogonal to the current direction of growth, which is set with the grow and grow' option (the latter option reverses the ordering of the children). The distance from the line to the parent node is given by the level distance.

\begin{tikzpicture} \path [help lines] node (root) {root} [grow=-10] child {node {1}}
child {node {2}}
child {node {3}}
child {node {4}};
\draw[|<->|,thick] (root-1.center)
-- node[above,sloped] {sibling distance} (root-2.center);
\draw[|<->|,thick] (root.center)
-- node[above,sloped] {level distance} +(-10:\tikzleveldistance);
\end{tikzpicture}

Here is a detailed description of the options:

- level distance=<distance> This option allows you to change the distance between different levels of the tree, more precisely, between the parent and the line on which its children are arranged. When given to a single child, this will set the distance for this child only.

  \begin{tikzpicture} \node {root} [level distance=20mm] child child {
  [level distance=5mm]
  child
  child
  child
  }
  child[level distance=10mm];
  \end{tikzpicture}

  \begin{tikzpicture} \tikzstyle{level 1}=[level distance=10mm] \tikzstyle{level 2}=[level distance=5mm] \node {root} child
  child {
  child
  child[level distance=10mm]
  child
  }
  child;
  \end{tikzpicture}

- sibling distance=<distance> This option specifies the distance between the anchors of the children of a parent node.

  \begin{tikzpicture}[level distance=4mm] \tikzstyle{level 1}=[sibling distance=8mm] \tikzstyle{level 2}=[sibling distance=4mm] \tikzstyle{level 3}=[sibling distance=2mm] \coordinate
  child {
  child {child child}
  child {child child}
  }
  child {
  child {child child}
  child {child child}
  };
  \end{tikzpicture}

  \begin{tikzpicture}[level distance=10mm] \tikzstyle{every node}=[fill=red!60,circle,inner sep=1pt] \tikzstyle{level 1}=[sibling distance=20mm, set style={{every node}+=[fill=red!45]}] \tikzstyle{level 2}=[sibling distance=10mm,
  set style={{every node}+=[fill=red!30]}]
  \tikzstyle{level 3}=[sibling distance=5mm,
  set style={{every node}+=[fill=red!15]}]
  \node {31}
  child {node {30}
  child {node {20}
  child {node {5}}
  child {node {4}}
  }
  child {node {10}
  child {node {9}}
  child {node {1}}
  }
  }
  child {node {20}
  child {node {19}
  child {node {1}}
  child[fill=none] {edge from parent[draw=none]}
  }
  child {node {18}}
  };
  \end{tikzpicture}

- grow=<direction> This option is used to define the <direction> in which the tree will grow. The <direction> can either be an angle in degrees or one of the following special text strings: down, up, left, right, north, south, east, west, north east, north west, south east, and south west. All of these have “their obvious meaning,” so, say, south west is the same as the angle -135o.

  As a side effect, this option installs the default growth function.

  In addition to setting the direction, this option also has a seemingly strange effect: It sets the sibling distance for the current level to 0pt, but leaves the sibling distance for later levels unchanged.

  This somewhat strange behaviour has a highly desirable effect: If you give this option before the list of children of a node starts, the “current level” is still the parent level. Each child will be on a later level and, hence, the sibling distance will be as specified originally. This will cause the children to be neatly aligned in a line orthogonal to the given <direction>. However, if you give this option locally to a single child, then “current level” will be the same as the child’s level. The zero sibling distance will then cause the child to be placed exactly at a point at distance level distance in the direction <direction>. However, the children of the child will be placed “normally” on a line orthogonal to the <direction>.

  These placement effects are best demonstrated by some examples:

  \tikz \node {root} [grow=right] child child;

  \tikz \node {root} [grow=south west] child child;

  \begin{tikzpicture}[level distance=10mm,sibling distance=5mm] \node {root} [grow=down] child child
  child[grow=right] {
  child child child
  };
  \end{tikzpicture}

  \begin{tikzpicture}[level distance=2em] \node {C} child[grow=up] {node {H}} child[grow=left] {node {H}} child[grow=down] {node {H}}
  child[grow=right] {node {C}
  child[grow=up] {node {H}}
  child[grow=right] {node {H}}
  child[grow=down] {node {H}}
  edge from parent[double]
  coordinate (wrong)
  };
  \draw[<-,red] ([yshift=-2mm]wrong) -- +(0,-1)
  node[below]{This is wrong!};
  \end{tikzpicture}

  \begin{tikzpicture} \node[rectangle,draw] (a) at (0,0) {start node}; \node[rectangle,draw] (b) at (2,1) {end}; \draw (a) -- (b) node[coordinate,midway] {}
  child[grow=100,<-] {node[above] {the middle is here}};
  \end{tikzpicture}

- grow'=<direction> This option has the same effect as grow, only the children are arranged in the opposite order.
- growth function=<macro name> This rather low-level option allows you to set a new growth function. The <macro name> must be the name of a macro without parameters. This macro will be called for each child of a node.

  The effect of executing the macro should be the following: It should transform the coordinate system in such a way that the origin becomes the place where the current child should be anchored. When the macro is called, the current coordinate system will be setup such that the anchor of the parent node is in the origin. Thus, in each call, the <macro name> must essentially do a shift to the child’s origin. When the macro is called, the TEX counter \tikznumberofchildren will be set to the total number of children of the parent node and the counter \tikznumberofcurrentchild will be set to the number of the current child.

  The macro may, in addition to shifting the coordinate system, also transform the coordinate system further. For example, it could be rotated or scaled.

  Additional growth functions are defined in the library, see Section 14.6.

#### 12.6 Edges From the Parent Node

Every child node is connected to its parent node via a special kind of edge called the edge from parent. This edge is added to the <child path> when the following path operation is encountered:

\path ... edge from parent[<options>] ...;

  This path operation can only be used inside <child paths> and should be given at the end, possibly followed by node specifications (we will come to that). If a <child path> does not contain this operation, it will be added at the end of the <child path> automatically.

  This operation has several effects. The most important is that it inserts the current “edge from parent path” into the child path. The edge from parent path can be set using the following option:

  - edge from parent path=<path> This options allows you to set the edge from parent path to a new path. The default for this path is the following:

    (\tikzparentnode\tikzparentanchor) -- (\tikzchildnode\tikzchildanchor)

    The \tikzparentnode is a macro that will expand to the name of the parent node. This works even when you have not assigned a name to the parent node, in this case an internal name is automatically generated. The \tikzchildnode is a macro that expands to the name of the child node. The two ...anchor macros are empty by default. So, what is essentially inserted is just the path segment (\tikzparentnode) -- (\tikzchildnode); which is exactly an edge from the parent to the child.

    You can modify this edge from parent path to achieve all sorts of effects. For example, we could replace the straight line by a curve as follows:

    \begin{tikzpicture}[edge from parent path= {(\tikzparentnode.south) .. controls +(0,-1) and +(0,1) .. (\tikzchildnode.north)}] \node {root} child {node {left}}
    child {node {right}
    child {node {child}}
    child {node {child}}
    };
    \end{tikzpicture}

    Further useful edge from parent paths are defined in the tree library, see Section 14.6.

    As said before, the anchors in the default edge from parent path are empty. However, you can set them using the following options:

    - child anchor=<anchor> Specifies the anchor where the edge from parent meets the child node by setting the macro \tikzchildanchor to .<anchor>.

      If you specify border as the <anchor>, then the macro \tikzchildanchor is set to the empty string. The effect of this is that the edge from the parent will meet the child on the border at an automatically calculated position.

      \begin{tikzpicture} \node {root} [child anchor=north] child {node {left} edge from parent[dashed]} child {node {right}
      child {node {child}}
      child {node {child} edge from parent[draw=none]}
      };
      \end{tikzpicture}

    - parent anchor=<anchor> This option works the same way as the child anchor, only for the parent.

  Besides inserting the edge from parent path, the edge from parent operation has another effect: The <options> are inserted directly before the edge from parent path and the following style is also installed prior to inserting the path:

  - style=edge from parent This style is inserted right before the edge from parent path and before the <options> are inserted. By default, it just draws the edge from parent, but you can use it to make the edge look different.

    \begin{tikzpicture} \tikzstyle{edge from parent}=[draw,red,thick] \node {root} child {node {left} edge from parent[dashed]} child {node {right}
    child {node {child}}
    child {node {child} edge from parent[draw=none]}
    };
    \end{tikzpicture}

  Note: The <options> inserted before the edge from parent path is added apply to the whole child path. Thus, it is not possible to, say, draw a circle in red as part of the child path and then have an edge to parent in blue. However, as always, the child node is a node and can be drawn in a totally different way.

  Finally, the edge from parent operation has one more effect: It causes all nodes following the operation to be placed on the edge. This is the same effect as if you had added the pos option to all these nodes, see also Section 11.6.1.

  As an example, consider the following code:

  \node (root) {} child {node (child) {} edge to parent node {label}};

  The edge to parent operation and the following node operation will, together, have the same effect as if we had said:

  (root) -- (child) node [pos=0.5] {label}

  Here is a more complicated example:

  \begin{tikzpicture} \node {root} child { node {left} edge from parent
  node[left] {a}
  node[right] {b}
  }
  child {
  node {right}
  child {
  node {child}
  edge from parent
  node[left] {c}
  }
  child {node {child}}
  edge from parent
  node[near end] {x}
  };
  \end{tikzpicture}

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